Analog-to-digital converters (ADCs) allow for an analog input signal to be sampled into the digital domain. ADCs have found wide-spread use in communications, as it allows the digitized signals to be processed with powerful digital signal processing (DSP) techniques. As electronic ADCs have developed, uses in RF-wireless communications such as cellular telephony and software defined radio have been made possible. ADCs in RF-wireless applications typically have high resolutions because bandwidth restrictions require the use of dense signal constellations. Other common uses for ADCs include instrumentation, such as high-speed real-time oscilloscopes, medical imaging, and radar.
Electronic ADC's have made steady technological progress, but issues such as clock-jitter and internal parameter mismatches make it difficult for ADCs to maintain high resolution as the sampling rate increases. It is common for ADC resolution to fall 1 bit for every factor of 2 rate increase.
Photonic technology can be used to aid in creating faster ADCs. The performance improvement is due to various factors depending on the specific design, but may stem, for instance, from the ability to generate ultra-short pulses with ultra-low timing jitter in the optical domain.
In addition to the standard Nyquist sampling, which is sampling at rates of at least two-times the highest frequency component of interest, there are times when subsampling or undersampling at lower sampling frequencies can be useful. Undersampling allows a very high carrier frequency to be digitized with a sample rate much less than twice the carrier frequency, but the sample rate must still be at least twice the total bandwidth the signal. This offers a possibility for simple, low cost, and low power consumption measurements of high frequency input signals. The low jitter and small aperture time of mode-locked lasers can be helpful in these applications. Although information over the signal bandwidth can be captured and digitized in this manner, there is information lost in the undersampling process. For instance, if the input frequency is simply a single frequency tone, then the measured carrier frequency of the signal is ambiguous. For some applications, measuring the carrier frequency or distinguishing between multiple frequencies is important. A method of undersampling with a nonuniform sampling period can resolve such ambiguities. One type of solution would be to use multiple optical wavelengths each having a different sampling frequency. This so-called compressive sampling regime has been demonstrated where the ambiguity can be resolved, including cases where there are multiple non-overlapping signal frequency bands to be measured. However, the cost and complexity of the scheme, as well as the complexity of the signal processing required (which slows down operation speed), may exclude it from many applications. Part of the expense is related to the need for the optical hardware, such as three separate optical pulse generators which may or may not require synchronization of their respective pulse rates. Synchronization adds additional expense to the system. In general optical ADC technology faces a cost hurdle since many types of implementations add substantial cost, size, and complexity in comparison to purely electronic ADCs. Thus finding simpler and lower cost implementations is of particular importance.
A method of pseudo-randomly sampling a signal, instead of using the more traditional periodic sampling, can also lead to resolving the ambiguity caused by under-sampling. The experimental realization of [10] uses optical sampling at pseudo-random sampling times to reconstruct the signal. However, the method used could be improved as to its complexity, cost, power consumption, and flexibility. For instance, in order to have fine resolution on the sampling time instances, the mode-locked laser must operate at a much higher repetition rate than the average sampling rate. This is non-optimal in terms of power consumption since almost all of the laser light is strongly attenuated to translate the high-rate optical pulses into a lower average rate pseudo-random stream of optical pulses. Also, it is difficult to change the time-grid which pulses are located on unless the mode-locked laser repetition frequency is widely tunable. Also, the high rate mode-locked laser is an expensive component. It's size, cost, and power consumption is often reduced in practice if passive mode-locking is used instead of active mode-locking, but many passive mode locking methods will not allow very high pulse repetition rates. The use of the external modulator adds cost, size, and power consumption in general. Employing lower rate mode-locked lasers or otherwise eliminating the high rate mode-locked laser is thus desirable.
It is known in the art that applying a high speed phase modulation to a pulse train can shift the pulse train's optical frequency or correspondingly its optical wavelength. Such a function has not previously been used in a photonic ADC.
What is needed is a photonic ADC capable of high resolution for signals with high carrier frequencies. Ideally it should be possible to determine from the digitized signal the input carrier frequency to a high accuracy over a very large frequency range. The configuration should be simple, robust, and low cost. Other practical concerns such as size, weight, and power consumption are also important and should be reduced if possible. It is useful it the system has a self-calibration and self-monitoring function to optimize and monitor the system performance in order to allow for very high resolution performance with modest component costs. It is advantageous if the nonuniform nature of the pulse sequence can be modified or reprogrammed by the user to suit a given input signal.